In the field of nuclear medical imaging technology, which includes PET imaging detector 100, as illustrated in FIG. 1, an array of radiation sensors, such as plurality of scintillators 106 and associated photosensors 102n, such as photomultiplier tubes (PMTs), avalanche photodiodes (APDs), or silicon photomultipliers (SiPMs) are usually arranged in a circle of a detector ring 106. Such a detector ring 106 surrounds a subject to be scanned. To conduct a so-called PET scan, a short-lived radioisotope, which decays by emitting a positron, is injected usually into the blood circulation of a living subject. After the metabolically active molecule becomes concentrated in tissues of interest, the research subject or patient is placed in the imaging scanner. The most commonly-used metabolically active molecule for this purpose is fluorodeoxyglucose (FDG), a sugar, which has a half life of 110 minutes. Note that other radiation sensors, such as solid state detectors could be used in the place of scintillators and photosensors.
As the radioisotope undergoes positron emission decay, it emits a positron, the antimatter counterpart of an electron. After traveling up to a few millimeters, the positron encounters and annihilates with an electron, producing a pair of gamma photons moving in almost opposite directions. These are detected when they reach one of a plurality of scintillation crystals in the scanning device, creating a burst of light detected by an array of photosensors. These bursts of light from a scintillator, such as Lutetium Orthosilicate (LSO) and Bismuth Germanate (BGO), have an intrinsic shape with a fast rising edge followed by a slow falling edge. The signals can be estimated as a function of:
                                          V            o                    ⁡                      (            t            )                          ≈                              A            1                    ·                      m            0                    ·                      (                                                            1                                      τ                    1                                                  ·                                  ⅇ                                                            -                      t                                        /                                          τ                      1                                                                                  -                                                1                                      τ                    0                                                  ·                                  ⅇ                                                            -                      t                                        /                                          τ                      0                                                                                            )                                              (        1        )            where τ0 is the characteristic scintillator decay time constant; and τ1 is mainly determined by the characteristics of the photosensor (such as PMT, APD, or SiPM), the open-loop gain of the first amplifier in the front-end electronics, and the input capacitance. When τ0>>τ1 (which are the cases for LSO and BGO crystals), τ1 dominates the rising edge of the pulse, and τ0 dominates the falling edge.
FIG. 1 illustrates a block diagram of the typical architecture of detectors and associated analog-to-digital-converters in a conventional system. Each matrix of photodetectors 112 produces a plurality of signals that can be processed to generate an image from a plurality of scintillation events that are detected by a photosensor 102. The photosensors 102 may be coupled to scintillators 106 through a lightguide 114. To determine the location of a detected annihilation, the system needs to accurately measure the timing and energy of both of the pair of oppositely traveling detected photons. Consequently a high amount of data has to be produced by the respective measurement circuits.
For example, as shown on the right side of FIG. 1, each scintillator has an associated matrix of detectors, such as photosensors 1021 . . . 102n, in this example are PMTs for illustration. Each signal of each PMT 1021 . . . 102n is first amplified by, for example, associated preamplifiers/buffers 1041 . . . 104n. The output signal of preamplifier/buffers 1041 . . . 104n can then be converted concurrently into discrete-time digital signals by associated analog-to-digital converters (ADC) 1081 . . . 108n. A sampling clock for each ADC be can provided at terminal 110. In this example, this digital processing architecture uses n independent ADC signals with peripheral circuitry to concurrently sample each of n photosensor signals per block.
The Laplace transfer-function of the signal described by Eq. 1 is:
                              H          ⁡                      (            s            )                          =                                            A              1                                      τ              1                                ·                      s                                          (                                  s                  +                                      1                                          τ                      0                                                                      )                            ·                              (                                  s                  +                                      1                                          τ                      1                                                                      )                                                                        (        2        )            
As can be seen in Eq. 2, the falling edge of the scintillation signal is a first-order exponential decay function, so the shape of the signal is always unipolar—it is either positive or negative depending on the polarity chosen for the sensor analog electronics. Based on a time recorded for when the scintillation signal reaches a threshold value, the system can determine the location of positron emission. Because the detection systems often filter the scintillation signal prior to comparing the signal to the threshold, a “time-walk” can occur, reducing the precision of the positron emission measurement. A time-walk is the shift in time between when the non-filtered signal crosses a threshold and when a filtered signal crosses the threshold, and can be caused either by processing delays and/or by a difference in the filtered pulse height.
FIG. 2 illustrates an example of time-walk error. In FIG. 2, the system receives an unfiltered signal 202, which the system then processes to yield a filtered signal 204. As illustrated, the filtered signal 204 normally has a lower peak value than the unfiltered signal 202. The difference between when the unfiltered signal 202 would have crossed a threshold 206 and when the filtered signal 204 crosses the threshold 206 is known as the time-walk error 208. Reducing this error can improve precision in recording positron emission measurements.